## Key Ideas > [!abstract] Core Concepts > > - **Erroneous beliefs that feel intuitively correct**: Students often unaware they hold misconceptions because they seem logical and persist without intervention (Vosniadou & Brewer, 1992) > - **Become entrenched through repeated practice**: Misconceptions embed in long-term memory when practised without corrective feedback, making them resistant to change (Chi, 2008) > - **Require cognitive conflict to address**: Simply informing students they're wrong is ineffective; teachers must demonstrate why existing beliefs are incorrect (Limón, 2001) ## Definition **Misconceptions**: Erroneous beliefs or incomplete knowledge that students hold, which tend to recur because they feel intuitively correct and students are often unaware they are incorrect (Smith, diSessa, & Roschelle, 1993). ## Connected To [[Mistakes]] | [[Diagnostic Questions]] | [[Formative Assessment]] | [[Schema]] | [[Prior Knowledge]] | [[Teach Methods that Last]] | [[Cognitive Load Theory]] --- ## Why misconceptions persist Misconceptions resist correction (Chi, 2008; Vosniadou & Brewer, 1992). Many misconceptions feel logical to students. Adding fractions by adding numerators and denominators separately ($\frac{1}{3} + \frac{1}{5} = \frac{2}{8}$) seems reasonable because it follows the pattern students know for whole numbers (Vosniadou & Brewer, 1992). Students don't realise their thinking is incorrect, so they don't seek correction (Smith et al., 1993). The misconception functions as their understanding of how things work. Without corrective feedback, misconceptions embed in long-term memory through rehearsal (Chi, 2008). Each time students practise the incorrect method, they strengthen the faulty schema. Some misconceptions work in limited contexts, which reinforces their perceived validity. This intermittent reinforcement makes them resistant to change (Siegler, 1996). ## Identification strategies Identifying misconceptions requires making student thinking visible. [[Formative Assessment]] strategies reveal student thinking whilst there's still time to address issues. Students must explain reasoning, not just provide answers. Misconceptions hide in unexplained correct answers copied from neighbours. [[Diagnostic Questions]] with carefully crafted distractors represent specific misconceptions. Wrong answers become informative. Track recurring errors across multiple students and contexts. When different students make the same mistake, it suggests a systematic misconception rather than random error. ## Addressing misconceptions through cognitive conflict Telling students they're wrong is ineffective because misconceptions feel intuitively correct (Limón, 2001). Create cognitive conflict that forces reconsideration (Festinger, 1957; Posner et al., 1982). Show why the existing belief leads to impossible or absurd conclusions. Make abstract misconceptions visible through specific cases where the faulty reasoning fails (Chi, 2008). After exposing the error, teach the correct approach and explain why it works (Posner et al., 1982). Students will not construct correct understanding from the failure of their misconception alone. ### Example: fraction addition misconception For students who add fractions by adding numerators and denominators, show that $\frac{1}{3} + \frac{1}{5} = \frac{2}{8} = \frac{1}{4}$ using their method. Point out that adding a positive number to $\frac{1}{3}$ somehow made it smaller, an impossibility. Have students explain why this must be incorrect. Show the proper common denominator approach and connect to fraction meaning and equivalent fractions. This takes longer than showing the correct method, but creates understanding that persists. ## Prevention strategies Choose mathematical representations that work across contexts, such as number lines for fractions rather than discrete models. Anticipate common errors and address them before they develop. Intervene quickly when misconceptions emerge. Ensure understanding of underlying concepts, not just procedures. ## Key warnings Informing students they're wrong rarely succeeds because misconceptions feel intuitively correct to them. Even after apparent correction, misconceptions can reappear under pressure such as exams or time constraints, when students revert to deeply embedded patterns. Some instructional shortcuts create misconceptions. For example, "borrowing" in subtraction suggests something is taken rather than regrouping. Teachers may not recognise misconceptions due to [[Curse of Knowledge]]. What's clearly wrong to experts can seem reasonable to novices. ## Practical examples Students think multiplication always makes numbers bigger. Address this with decimal and fraction multiplication. "BODMAS means always do brackets first" can be countered with examples where the operation inside brackets must wait. "Negative numbers are smaller" can be addressed using number line and temperature contexts. "Area and perimeter are related" can be countered by showing rectangles with same area but different perimeters. ## References Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. In S. Vosniadou (Ed.), *International handbook of research on conceptual change* (pp. 61-82). Routledge. Festinger, L. (1957). *A theory of cognitive dissonance*. Stanford University Press. Limón, M. (2001). On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal. *Learning and Instruction*, 11(4-5), 357-380. https://doi.org/10.1016/S0959-4752(00)00037-2 Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. *Science Education*, 66(2), 211-227. https://doi.org/10.1002/sce.3730660207 Siegler, R. S. (1996). *Emerging minds: The process of change in children's thinking*. Oxford University Press. Smith, J. P., diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. *The Journal of the Learning Sciences*, 3(2), 115-163. https://doi.org/10.1207/s15327809jls0302_1 Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. *Cognitive Psychology*, 24(4), 535-585. https://doi.org/10.1016/0010-0285(92)90018-W